Lim x>0 - ((x+deltaX) ^2+x+deltaX - (x^2+x)) / deltaX

Question

Vanessa Velasquez

Mathematics

10 September, 00:00

Lim x>0 - ((x+deltaX) ^2+x+deltaX - (x^2+x)) / deltaX

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Ariel Mcintyre · Answer 1

((x+deltaX) ^2+x+deltaX - (x^2+x)) / deltaX = (x^2 + 2x delta x + (delta x) ^2 + x + delta x - x^2 - x) / delta x = delta x (2x + delta x + 1) / delta x = 2x + delta x + 1

Therefore, Lim as x tends to 0 of ((x + delta X) ^2 + x + deltaX - (x^2 + x)) / deltaX = 1 + delta x